Let f be a real-valued function of a real variable defined as f(x) = x2 for x ≥ 0, and f(x) = -x2 for x < 0.
Which one of the following statements is true?
1
f(x) is discontinuous at x = 0
2
f(x) is continuous but not differentiable at x = 0.
3
f(x) is differentiable but its first derivative is not continuous x = 0.
4
f(x) is differentiable but its first derivative is not differentiable at x = 0.